Problem: Solve for $x$ : $x^2 + 4x + 3 = 0$
Answer: The coefficient on the $x$ term is $4$ and the constant term is $3$ , so we need to find two numbers that add up to $4$ and multiply to $3$ The two numbers $3$ and $1$ satisfy both conditions: $ {3} + {1} = {4} $ $ {3} \times {1} = {3} $ $(x + {3}) (x + {1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x + 1) = 0$ $x + 3 = 0$ or $x + 1 = 0$ Thus, $x = -3$ and $x = -1$ are the solutions.